Truncated 6-simplexes


In six-dimensional geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex.
There are unique 3 degrees of truncation. Vertices of the truncation 6-simplex are located as pairs on the edge of the 6-simplex. Vertices of the bitruncated 6-simplex are located on the triangular faces of the 6-simplex. Vertices of the tritruncated 6-simplex are located inside the tetrahedral cells of the 6-simplex.

Truncated 6-simplex

Alternate names

The vertices of the truncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the truncated 7-orthoplex.

Images

Bitruncated 6-simplex

Alternate names

The vertices of the bitruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the bitruncated 7-orthoplex.

Images

Tritruncated 6-simplex

The tritruncated 6-simplex is an isotopic uniform polytope, with 14 identical bitruncated 5-simplex facets.
The tritruncated 6-simplex is the intersection of two 6-simplexes in dual configuration: and.

Alternate names

The vertices of the tritruncated 6-simplex can be most simply positioned in 7-space as permutations of. This construction is based on facets of the bitruncated 7-orthoplex. Alternately it can be centered on the origin as permutations of.

Images

Related polytopes

Related uniform 6-polytopes

The truncated 6-simplex is one of 35 uniform 6-polytopes based on the Coxeter group, all shown here in A6 Coxeter plane orthographic projections.